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Here is my new logic puzzle.
I thought of a positive integer that is below 100 and is divisible by 7. In addition to the public knowledge above, I privately tell the units digit of my number to Alice and the tens digit to Bob. Alice and Bob are very logical people, but their conversation might seem strange:

The solution with number 70 is a posible solution, but is not completely satisfying as it doesn't explain some features of the puzzle: why Alice speaks, why the puzzle states that they are "very logical" people, why the conversation "might seem strange".

Once the information of the text is acquired and the first analisis is done becomes clear that the puzzle is centered on the numbers 7,70,77 and on the meaning of the conversation between Alice and Bob.

This meaning depends heavily on the context of the conversation, which is left to the reader. Different contexts of the above conversation lead to different solutions (also in the absence of any Knights and Lyars supposition). There is difference if Alice is testing Bob ability in logic, if she is aiming to hide the number from Bob or viciversa, or if she wants to collect information from Bob...)

For example if Tanya's number is 70 and Alice's aim (who knows the number by the 0 digit) is not to share with Bob her knowledge or the number (and Bob suspects it), the phrase "You do not know..." takes a very different meaning, as Alice is apparently leading Bob to the right number, but the deeper intention is to induce Bob to dismiss it. There could be different scenarios like this.

All of this thoughts lead to two ideas:

As the context have a weight on the solution and is left to the reader, the solution of the puzzle is open.

As Alice and Bob are very logic people every attempt of one or the other to confuse the partner (in a simple matter like this which involves just three numbers) can be anticipate or use by the other to take advantage and finally leads to nothing. Alice and Bob know this, so that no conversation should take place, except if Alice and Bob pursue two different, non opposite, agendas in the conversation.